1. Quantum Theory and the Atom
Electrons in Atoms and the Periodic Table

2. Daily Review Describe Bohr’s contribution to atomic theory.
What is the name of this model.
How many orbits are found in this model?

3. Learning Goals Discuss the Bohr Model
Relate wavelength and frequency to the Bohr Model
Calculate Wavelength and Frequency

4. Bohr’s Model of the Atom
Einstein’s theory of light’s dual nature accounted for several unexplainable phenomena, but it did not explain why atomic emission spectra of elements were discontinuous.

5. Bohr’s Model of the Atom
In 1913, Niels Bohr, a Danish physicist working in Rutherford’s laboratory, proposed a quantum model for the hydrogen atom that seemed to answer this question.
This model correctly predicted the frequency lines in hydrogen’s atomic emission spectrum.

7. Bohr’s Model of the Atom
The lowest allowable energy state of an atom is called its ground state.
When an atom gains energy, it is in an excited state.

8. Bohr’s Model of the Atom
Bohr suggested that an electron moves around the nucleus only in certain allowed circular orbits.

9. Bohr’s Model of the Atom
Each orbit was given a number, called the quantum number.
Bohr orbits are like steps of a ladder, each at a specific distance from the nucleus and each at a specific energy.

10. Bohr’s Model of the Atom
Hydrogen’s single electron is in the n = 1 orbit when it is in the ground state.
When energy is added, the electron moves to the n = 2 orbit.

11. Bohr’s Model of the Atom
The electron releases energy as it falls back towards the ground state and releases light.

12. Bohr’s Model of the Atom
Bohr’s model explained the hydrogen’s spectral lines, but failed to explain any other element’s lines.
For this and other reasons, the Bohr model was replaced with a more sophisticated model called the quantum-mechanical or wave- mechanical model.  

13. A look back…. Underline the section in your notes that:
Relates frequency and the emissions spectra
Defines ground state
Discusses HOW energy is released and absorbed in this model
What Bohr’s model failed to explain

14. Waves Wavelength () - length of one complete wave
Frequency () - # of waves that pass a point during a certain time period
hertz (Hz) = 1/s
Amplitude (A) - distance from the origin to the trough or crest f
Wave — a periodic oscillation that transmits energy through space
Characteristic properties of waves
1. Waves are periodic.
– They repeat regularly in both space and time.
2. Wavelength
– Distance between two corresponding points in a wave
– Symbolized by 
– Described by any appropriate unit of distance
3. Frequency of a wave
– Number of oscillations that pass a particular point in a given period of time
– Represented by the symbol 
– Units are oscillations per second or 1/s = s-1, which is called the hertz (Hz)
4. Amplitude, or vertical height, of a wave
– Defined as half the peak-to-trough height
– As the amplitude of a wave with a given frequency increases, so does its energy
– Two waves can have the same amplitude but different wavelengths
5. Speed
– Distance traveled by a wave per unit of time
– Represented by the symbol 
– Measured in meters per second (m/s)
– Speed of a wave is equal to the product of its wavelength and frequency
(wavelength) (frequency) = speed
 = 
(meters) (waves) = meters
(waves) (second) second
Courtesy Christy Johannesson

15.  A  greater frequency (color) greater amplitude (intensity)
Courtesy Christy Johannesson

16. Electromagnetic Spectrum
Visible spectrum
HIGH
ENERGY
Violet
Blue
Green
Yellow
Orange
Red
LOW
ENERGY
400 nm
500 nm
600 nm
700 nm
White
Light
g rays
X-rays
Ultraviolet
Infrared
Microwave
Radio waves
Water waves transmit energy through space by the periodic oscillation of matter.
• Energy that is transmitted, or radiated, through space in the form of periodic oscillations of an electric and a magnetic field is called electromagnetic radiation.
Electromagnetic radiation
– Consists of two perpendicular waves, one electric and one magnetic, propagates at the speed of light, abbreviated c, and has a value of x 108 m/s
– Is radiant energy that includes radio waves, microwaves, visible light, X -rays, and gamma rays
– Various kinds of electromagnetic radiation all have the same speed (c) but differ in wavelength and frequency
– Frequency of electromagnetic radiation is inversely proportional to the wavelength
c =  or  = c/
– Energy of electromagnetic radiation is directly proportional to its frequency (E  ) and inversely proportional to its wavelength (E  1/)
Radar TV FM
Short
Wave
Long
Wave
10-2nm
10-1nm
100nm
101nm
102nm
103nm
10-3cm
10-2cm
10-1cm
100cm
101cm
1cm
101m
102m
103m
104m
Wavelength, l
1019Hz
1018Hz
1017Hz
1016Hz
1015Hz
1014Hz
1013Hz
1012Hz
1011Hz
1010Hz
109Hz
100 MHz
10 MHz
1 MHz
100 KHz
Frequency, n
Electromagnetic spectrum
Davis, Frey, Sarquis, Sarquis, Modern Chemistry 2006, page 98

17. Wavelength and Frequency
“nu” “lambda”
c = speed of light (3 x 108 m/s)
= frequency (s-1)
l = wavelength (m)
c = n l
E = h n
E = energy (Joules or J)
h = Planck’s constant (6.6 x10-34 J/s)
= frequency (s-1)

18. Electromagnetic Spectrum
EX: Find the frequency of a photon with a wavelength of 434 nm.
GIVEN:
n = ?
 = 434 nm
= 4.34  10-7 m
c = 3.00  108 m/s
WORK:
1 m
1 x 109 nm
f = 3.00  108 m/s
4.34  10-7 m
f = 6.91  1014 Hz
Courtesy Christy Johannesson

20. The Quantum Mechanical Model
Day 2

21. Daily Review Draw the Bohr Model and
Label energy levels (quantum levels)
Label the nucleus
Label two electrons in the ground state
Label the excited state.
Explain how the electron moves to the excited state.
Explain how energy is released

22. Learning Goals
Explain the impact of de Broglie’s wave particle duality and the Heisenberg uncertainty principle on the current view of electrons in atoms.
Identify the relationships among a hydrogen atom’s energy levels, sublevels, and atomic orbitals.
Compare and contrast the Bohr and QM models.

23. Quantum Mechanical Model
Louis de Broglie (1892–1987) hypothesized that particles, including electrons, could also have wavelike behaviors.
Electrons do not behave like particles flying through space.
We cannot, in general, describe their exact paths.

24. Quantum Mechanical Model
Heisenberg showed it is impossible to take any measurement of an object without disturbing it.
The Heisenberg uncertainty principle states that it is fundamentally impossible to know precisely both the velocity and position of a particle at the same time.

26. Quantum Mechanical Model
The only quantity that can be known is the probability for an electron to occupy a certain region around the nucleus.

27. Quantum Mechanical Model
Schrödinger treated electrons as waves in a model called the quantum mechanical model of the atom.
Schrödinger’s equation applied equally well to elements other than hydrogen (unlike Bohr’s model).

28. Quantum Mechanical Model
The quantum mechanical model makes no attempt to predict the path of an electron around the nucleus.
Bohr orbits were replaced with quantum-mechanical orbitals.

29. Quantum Mechanical Model
Orbitals are different from orbits in that they represent probability maps that show a statistical distribution of where the electron is likely to be found.

30. Quantum Mechanical Model
In the quantum-mechanical model, a number and a letter specify an orbital.
The lowest-energy orbital is called the 1s orbital.
It is specified by the number 1 and the letter s.

31. Hydrogen’s Atomic Orbitals
The number is called the Principal quantum number (n) and it indicates the relative size and energy of atomic orbitals.
n specifies the atom’s major energy levels, called the principal energy levels.

32. Hydrogen’s Atomic Orbitals
Energy sublevels are contained within the principal energy levels.

33. Hydrogen’s Atomic Orbitals
Each energy sublevel relates to orbitals of different shape.
s, p, d, f
s, p, d
s, p s

34. Hydrogen’s Atomic Orbitals
s sublevel:

35. Hydrogen’s Atomic Orbitals
p sublevel:

36. Hydrogen’s Atomic Orbitals
d sublevel:

37. Hydrogen’s Atomic Orbitals
f sublevel:

39. Hydrogen’s Atomic Orbitals
Orbitals are sometimes represented by dots, where the dot density is proportional to the probability of finding the electron.
The dot density for the 1s orbital is greatest near the nucleus and decreases farther away from the nucleus.
The electron is more likely to be found close to the nucleus than far away from it.

41. Hydrogen’s Atomic Orbitals

42. Hydrogen’s Atomic Orbitals
At any given time, hydrogen’s electron can occupy just one orbital.
When hydrogen is in the ground state, the electron occupies the 1s orbital.
When the atom gains a quantum of energy, the electron is excited to one of the unoccupied orbitals.